venn diagram

Venn Diagram

How to diagram A, E, I, O.

First of all, make sure that you and your listeners/readers are using the same method of notation because there is more than one method of making a Venn diagram.

The method introduced here is to use

1. shading to represent an empty area; and

2. a small cross to represent the existence of one element in a certain area.

All S are P. (A)No S are P. (E)

Shade out the area of S that is outside P.Shade out the area of S that overlaps P.

Some S are P. (I)Some S are not P. (O)

Put a cross in the intersected area of S and P.Put a cross in the area of S but outside P.

An example on how to use Venn Diagram to demonstrate whether or not an argument is valid.

Some famous professors are old people.Some F are O.

All bespectacled people are famous professors.All B are F.

So, some old people are bespectacled people.So, some O are B.

Firstly, draw the three circles representing the three classes F, O and B.

Then, draw the first premise “Some F are O” (i.e. put a cross in the intersected area of F and O, but the cross should be put on the line because at this stage you are unsure which side the small will be.)

Thirdly, draw the second premise “All B are F” (i.e. shade out the area of B that is outside F.)

Lastly, we do NOT draw the conclusion but we use a different colour (for example I use red lines in the class) or use thick lines (I use thick lines because it’d be easier for me to handle all the files in black and white) to show the conclusion: in our example, in order to diagram the conclusion, there must be a cross within the thick-lined area. But we see that the cross is only on the boundary, NOT within the thick-lined area.

Since the information provided by the premises do not cover the information presented in the conclusion; it means that even if the premises are true, there is a chance that the conclusion is false. Hence, the argument is INV ALID.

(Note that if the drawing of the premises already covers the conclusion, the argument will be valid.)